Banach and counting measures, and dynamics of singular quantum states generated by averaging of operator random walks

Quantum Physics [Submitted on 26 Mar 2026] Banach and counting measures, and dynamics of singular quantum states generated by averaging of operator random walks E. A. Dzhenzher, S. V. Dzhenzher, V. Zh. Sakbaev In this paper the random channels and their compositions in the space of quantum states are studied. For compositions of i.i.d. random unitary channels, the limit behaviour of probability distributions is described. The sufficient condition for convergence in probability is obtained. The generalized convergence in distribution w.r.t. weak operator topology is obtained. The analysis of transmission of pure and normal states to the set of singular states is done. The dynamics of quantum states is described in terms of the evolution of the values of quadratic forms of operators from the algebra that implements the representation of canonical commutation relations. Comments: 14 pages, no figures Subjects: Quantum Physics (quant-ph); Functional Analysis (math.FA) Cite as: arXiv:2603.25151 [quant-ph]   (or arXiv:2603.25151v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.25151 Focus to learn more Submission history From: Sviatoslav Dzhenzher [view email] [v1] Thu, 26 Mar 2026 08:12:43 UTC (23 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: math math.FA References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)